If you are getting voltage at BOTH the push on relay terminals, you have found part of the problem. One terminal receives battery voltage "in start" from the key, that wire comes out of the bulkhead connector. The remaining terminal connects to a wire which runs down over the top of the transmission, and grounds via the neutral safety switch
First thing to do is simply hold the key in "start" with one hand, and work the shifter from park to neutral and back "jiggle and wiggle" If it tries to start or at least clicks, your linkage is likely out of adjustment